From TARDIS Index File, the free Doctor Who reference.

The Roman Empire was a large, dictatorial state that existed in Europe for about four centuries, starting a few decades before the birth of Jesus Christ. It was centered in the city of Rome, though it encompassed cities like Pompeii and Byzantium and had a presence as far as Cardiff, where a Roman fort was situated.

One of Scaroth's temporal splinters is known to have posed as a high-ranking Roman, possibly even an emperor. (DW: City of Death)

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The Roman Empire (Latin: Imperium Romanum) was an ancient nation state on Earth, which existed from the 1st century BCE until September 4, 476 when the final Roman Emperor was deposed. The capital of the Empire was the city of Rome, and the state succeeded the Roman Republic, which had lasted from the 5th to the 1st centuries BCE.

At its peak, the Roman Empire controlled most of Europe, as well as portions of Asia and Africa. The Roman Empire at its largest controlled 5,900,000 square kilometers of territory.

However after reaching it's greatest extent the Empire began a long, slow decline. The city of Rome was sacked in 410, during the reign of Emperor Honorius, and subsequently fell before the end of the century. Almost 2,000 years later, during the Borg crisis of 2366, CaptainJean-Luc Picard wondered if Honorius was truly cognizant of the fact that his Empire was collapsing while his capital was being sacked. (TNGepisode: "The Best of Both Worlds")

The Roman Empire played a major role in the history of Earth, with its influences in areas such as culture, law, language, government, and architecture continuing into the 24th century.

On the planet 892-IV, or Magna Roma, the culture developed a parallel Roman Empire, which did not fall and existed for at least 20 centuries. This parallel Empire reached a level of technology similar to that of 20th century Earth by the time the USS Enterprise visited the planet in 2268. (TOSepisode: "Bread and Circuses") It was later theorized that the Preservers had taken a number of Earth Romans and seeded that world with these people, who established their Empire on that world. (TOSnovel: Ex Machina)

After the visit of the USS Enterprise to Pollux II, it was theorized that the Beings had visited other worlds in addition to Earth, such as Vulcan and perhaps Romulus as well. This theory provided a possible reason why Romulan culture was so similar to the culture of the Roman Empire. (Startrek.com article Strange Relations: Romulans and Vulcans)